Mathematics Behind Wiggly Worm Knots Could Inspire Shapeshifting Robotics

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Unraveling the Mathematics Behind Wiggly Worm Knots

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California black worms tightly tangled collectively in a blob. Research into the distinctive tangling and untangling behaviors of California blackworms may affect the design of superior, shapeshifting robotics, in keeping with a collaborative examine by Georgia Tech and MIT researchers. Credit: Georgia Institute of Technology

Georgia Tech and MIT researchers have used ultrasound imaging and meticulous data tracking to understand the rapid tangling and untangling behaviors of California blackworms. Their study, which provided the first mathematical model of these behaviors, could inspire the design of advanced, shapeshifting robotics and multifunctional materials.

For millennia, humans have used knots for all kinds of reasons — to tie rope, braid hair, or weave fabrics. But there are organisms that are better at tying knots and far superior — and faster — at untangling them.

Tiny California blackworms intricately tangle themselves by the thousands to form ball-shaped blobs that allow them to execute a wide range of biological functions. But, most striking of all, while the worms tangle over a period of several minutes, they can untangle in mere milliseconds, escaping at the first sign of a threat from a predator.

Saad Bhamla, assistant professor in the School of Chemical and Biomolecular Engineering at Georgia Tech, wanted to understand precisely how the blackworms execute their tangling and untangling movements. To investigate, Bhamla and a team of researchers at Georgia Tech linked up with mathematicians at MIT. Their research, published on April 27 in the journal Science, could influence the design of fiber-like, shapeshifting robotics that self-assemble and move in ways that are fast and reversible. The study also highlights how cross-disciplinary collaboration can answer some of the most perplexing questions in disparate fields.

Capturing the Inside of a Worm Blob

Fascinated by the science of ultrafast motion and collective conduct, Bhamla and Harry Tuazon, a graduate scholar in Bhamla’s lab, have studied California blackworms for years, observing how they use collective motion to kind blobs after which disperse.

“We wanted to understand the exact mechanics behind how the worms change their movement dynamics to achieve tangling and ultrafast untangling,” Bhamla stated. “Also, these are not just typical filaments like string, ethernet cables, or spaghetti — these are living, active tangles that are out of equilibrium, which adds a fascinating layer to the question.”

Worm Ball Untangled

A blob of worms untangling at ultrafast pace. Credit: Georgia Institute of Technology

Tuazon, a co-first writer of the examine, collected movies of his experiments with the worms, together with macro movies of the worms’ collective dispersal mechanism and microscopic movies of 1, two, three, and several other worms to seize their actions.

“I was shocked when I pointed a UV light toward the worm blobs and they dispersed so explosively,” Tuazon stated. “But to understand this complex and mesmerizing maneuver, I started conducting experiments with only a few worms.”

“Knots and tangles are a fascinating area where physics and mechanics meet some very interesting math. These worms seemed like a good playground to investigate topological principles in systems made up of filaments.” — Vishal Patil

Bhamla and Tuazon approached MIT mathematicians Jörn Dunkel and Vishal Patil (a graduate scholar on the time and now a postdoctoral fellow at Stanford University) a few collaboration. After seeing Tuazon’s movies, the 2 theorists, who focus on knots and topology, have been keen to affix.

“Knots and tangles are a fascinating area where physics and mechanics meet some very interesting math,” stated Patil, co-first writer on the paper. “These worms seemed like a good playground to investigate topological principles in systems made up of filaments.”

A key second for Patil was when he seen Tuazon’s video of a single worm that had been provoked into the escape response. Patil observed the worm moved in a figure-eight sample, turning its head in clockwise and counterclockwise spirals as its physique adopted.

Worm Swimming Figure 8

A single California black worm strikes in a helical gait. Credit: Georgia Institute of Technology

The researchers thought this helical gait sample would possibly play a task within the worms’ capacity to tangle and untangle. But to mathematically quantify the worm tangle buildings and mannequin how they braid round one another, Patil and Dunkel wanted experimental information.

Bhamla and Tuazon set about to search out an imaging approach that will permit them to see contained in the worm blob so they may collect extra information. After a lot trial and error, they landed on an surprising resolution: ultrasound. By putting a dwell worm blob in unhazardous jelly and utilizing a business ultrasound machine, they have been lastly capable of observe the within of the intricate worm tangles.

“Capturing the inside structure of a live worm blob was a real challenge,” Tuazon stated. “We tried all sorts of imaging techniques for months, including X-rays, confocal microscopy, and tomography, but none of them gave us the real-time resolution we needed. Ultimately, ultrasound turned out to be the solution.”

After analyzing the ultrasound movies, Tuazon and different researchers in Bhamla’s lab painstakingly tracked the motion of the worms by hand, plotting greater than 46,000 information factors for Patil and Dunkel to make use of to grasp the arithmetic behind the actions.

Explaining Tangling and Untangling

Answering the questions of how the worms untangle shortly required a mixture of mechanics and topology. Patil constructed a mathematical mannequin to clarify how helical gaits can result in tangling and untangling. By testing the mannequin utilizing a simulation framework, Patil was capable of create a visualization of worms tangling.

The mannequin predicted that every worm shaped a tangle with at the very least two different worms, revealing why the worm blobs have been so cohesive. Patil then confirmed that the identical class of helical gaits may clarify how they untangle. The simulations have been uncanny of their resemblance to actual ultrasound photographs and confirmed that the worms’ alternating helical wave motions enabled the tangling and the ultrafast untangling escape mechanism.

“What’s striking is these tangled structures are extremely complicated. They are disordered and complex structures, but these living worm structures are able to manipulate these knots for crucial functions,” Patil stated.

“Just as the worm blobs perform remarkable tangling and untangling feats, so may future bioinspired materials defy the limits of conventional structures by exploiting the interplay between mechanics, geometry, and activity.” — Eva Kanso

While it has been identified for many years that the worms transfer in a helical gait, nobody had ever made the connection between that motion and the way they escape. The researchers’ work revealed how the mechanical actions of particular person worms decide their emergent collective conduct and topological dynamics. It can also be the primary mathematical principle of energetic tangling and untangling.

“This remark might appear to be a mere curiosity, however its implications are far-reaching. Active filaments are ubiquitous in organic buildings, from DNA strands to entire organisms,” said Eva Kanso, program director at the National Science Foundation and professor of mechanical engineering at the University of Southern California.

Mathematics Behind Wiggly Worm Knots

Simulation of worms untangling (left) and tangling (right). Credit: Massachusetts Institute of Technology

“These filaments serve myriads of functions and can provide a general motif for engineering multifunctional structures and materials that change properties on demand. Just as the worm blobs perform remarkable tangling and untangling feats, so may future bioinspired materials defy the limits of conventional structures by exploiting the interplay between mechanics, geometry, and activity.”

Looking Forward

The researchers’ model demonstrates the advantages of different types of tangles, which could allow for programming a wide range of behaviors into multifunctional, filament-like materials, from polymers to shapeshifting soft robotic systems. Many companies, such as 3M, already use nonwoven materials made of tangling fibers in products, including bandages and N95 masks. The worms could inspire new nonwoven materials and topological shifting matter.

“Actively shapeshifting topological matter is currently the stuff of science fiction,” said Bhamla. “Imagine a soft, nonwoven material made of millions of stringlike filaments that can tangle and untangle on command, forming a smart adhesive bandage that shape-morphs as a wound heals, or a smart filtration material that alters pore topology to trap particles of different sizes or chemical properties. The possibilities are endless.”

Reference: “Ultrafast reversible self-assembly of living tangled matter” by Vishal P. Patil, Harry Tuazon, Emily Kaufman, Tuhin Chakrabortty, David Qin, Jörn Dunkel and M. Saad Bhamla, 27 April 2023, Science.
DOI: 10.1126/science.ade7759

In addition to Bhamla, Tuazon, Patil, and Dunkel, Georgia Tech researchers Emily Kaufman, Tuhin Chakrabortty, and David Qin contributed to this study.